Beurling-Komatsu回火超分布空间的核定理
Kernel theorem for the space of Beurling - Komatsu tempered ultradistibutions
摘要：
利用Beurling-Komatsu型调和超分布空间元素的Fourier-Hermite系数的特征，给出了该空间的核定理的一个简单证明.本文详细证明了Beurling-Komatsu型调和超分布的检验空间可等同于超多项式下降序列空间，其对偶空间可等同于超多项式增长序列空间。作为核定理的结果，我们得到Weyl变换可以在Beurling-Komatsu型回火超分布空间上推广。
英文摘要：
We give a simple proof of the Kernel theorem for the space of tempered ultradistributions of Beurling - Komatsu type, using the characterization of Fourier-Hermite coefficients of the elements of the space. We prove in details that the test space of tempered ultradistributions of Beurling - Komatsu type can be identified with the space of sequences of ultrapolynomal falloff and its dual space with the space of sequences of ultrapolynomial growth. As a consequence of the Kernel theorem we have that the Weyl transform can be extended on a space of tempered ultradistributions of Beurling - Komatsu type.
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